I want to add two IEEE 754 numbers. I followed the steps to add two 754 numbers. However the result it not correct. Number 1: S:0 E:01111111 M:11111111111111111111111

Number 2: S:0 E:01111111 M:00000000000000000000000

Here is my calculation:

enter image description here

The site http://weitz.de/ieee/ gives this result: S: 0 E: 10000000 M: 10000000000000000000000

in my calculation the mantissa is 01111... Why?

  • $\begingroup$ If you have more than 10 bits, it's very helpful to add a space between groups of four bits. $\endgroup$
    – gnasher729
    Aug 14, 2020 at 8:04
  • $\begingroup$ In their calculation I see the same mantissa as yours. $\endgroup$
    – plop
    Aug 14, 2020 at 11:16
  • $\begingroup$ What about number of bits & rounding? $\endgroup$
    – greybeard
    Aug 15, 2020 at 7:01
  • 3
    $\begingroup$ Just rounding. Tere is one extra 1 on the right of the mantissa, with rounding 01111... becomes 10000..... $\endgroup$
    – Grabul
    Sep 13, 2020 at 9:17
  • $\begingroup$ I’m voting to close this question because it is about one person making a mistake or misunderstanding something, and any answer would be completely useless for anyone else. Including OP who probably hasnt been stuck in this problem for three years. $\endgroup$
    – gnasher729
    Jan 28 at 16:51

2 Answers 2


You forgot the implicit leading 1 in the mantissa. The mantissa is not 23 bits, it's 24 bits with a 1 as the leading bit.

  • 2
    $\begingroup$ i did not forgot it. 1,111... and 1,000 $\endgroup$
    – otto
    Aug 14, 2020 at 8:13
  • $\begingroup$ Where do these 1,111... and 1,000 come from ?? $\endgroup$
    – user16034
    Sep 5, 2022 at 13:46

$$\begin{align}1&.01111111 \\+1&.11111111111111111111111\\=11&.01111110111111111111111\end{align}$$

You obtain the same result with the calculator.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.